Flow Measurement: An Inverse Problem Formulation

TL;DR

This paper introduces a novel inverse problem approach for flow measurement using wave equations and partial boundary data, providing a mathematically rigorous and computationally efficient method validated by numerical simulations.

Contribution

It presents the first mathematical model for flow measurement based on PDEs, with a well-posed formulation and an efficient algorithm for recovering flow fields from boundary measurements.

Findings

Model is mathematically well-posed

Algorithm accurately recovers flow fields

Demonstrates robustness across scenarios

Abstract

This paper proposes a new mathematical formulation for flow measurement based on the inverse source problem for wave equations with partial boundary measurement. Inspired by the design of acoustic Doppler current profilers (ADCPs), we formulate an inverse source problem that can recover the flow field from the observation data on a few boundary receivers. To our knowledge, this is the first mathematical model of flow measurement using partial differential equations. This model is proved well-posed, and the corresponding algorithm is derived to compute the velocity field efficiently. Extensive numerical simulations are performed to demonstrate the accuracy and robustness of our model. Our formulation is capable of simulating a variety of practical measurement scenarios.